Here’s an example problem for finding inverse functions:

Problem:

The function $f(x) = \frac{3x - 2}{x + 1}$ is defined for all $x \neq -1$.

1. Find the inverse function, $f^{-1}(x)$, if it exists.
2. State the domain and range of both $f(x)$ and $f^{-1}(x)$.

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Let me know when you're ready for the solution or if you have any questions!

Here are 5 related questions to expand your understanding:

1. What conditions must be met for a function to have an inverse?
2. How do you verify that two functions are inverses of each other?
3. What happens if a function is not one-to-one? Can it still have an inverse?
4. How do domain restrictions affect the existence of an inverse function?
5. Can you find the inverse of $f(x) = x^2$ if the domain is $x \geq 0$?

Tip:

When solving for the inverse, swap $x$ and $y$ (where $y = f(x)$) and solve for $y$ to find $f^{-1}(x)$.